by Yiu Ming Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 92-99). / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Bayesian YING-YANG Learning Theory and Number Selec- tion Criterion --- p.5 / Chapter 1.2 --- General Motivation --- p.6 / Chapter 1.3 --- Contributions of the Thesis --- p.6 / Chapter 1.4 --- Other Related Contributions --- p.7 / Chapter 1.4.1 --- A Fast Number Detection Approach --- p.7 / Chapter 1.4.2 --- Application of RPCL to Prediction Models for Time Series Forecasting --- p.7 / Chapter 1.4.3 --- Publications --- p.8 / Chapter 1.5 --- Outline of the Thesis --- p.8 / Chapter 2 --- Open Problem: How Many Clusters? --- p.11 / Chapter 3 --- Bayesian YING-YANG Learning Theory: Review and Experiments --- p.17 / Chapter 3.1 --- Briefly Review of Bayesian YING-YANG Learning Theory --- p.18 / Chapter 3.2 --- Number Selection Criterion --- p.20 / Chapter 3.3 --- Experiments --- p.23 / Chapter 3.3.1 --- Experimental Purposes and Data Sets --- p.23 / Chapter 3.3.2 --- Experimental Results --- p.23 / Chapter 4 --- Conditions of Number Selection Criterion --- p.39 / Chapter 4.1 --- Alternative Condition of Number Selection Criterion --- p.40 / Chapter 4.2 --- Conditions of Special Hard-cut Criterion --- p.45 / Chapter 4.2.1 --- Criterion Conditions in Two-Gaussian Case --- p.45 / Chapter 4.2.2 --- Criterion Conditions in k*-Gaussian Case --- p.59 / Chapter 4.3 --- Experimental Results --- p.60 / Chapter 4.3.1 --- Purpose and Data Sets --- p.60 / Chapter 4.3.2 --- Experimental Results --- p.63 / Chapter 4.4 --- Discussion --- p.63 / Chapter 5 --- Application of Number Selection Criterion to Data Classification --- p.80 / Chapter 5.1 --- Unsupervised Classification --- p.80 / Chapter 5.1.1 --- Experiments --- p.81 / Chapter 5.2 --- Supervised Classification --- p.82 / Chapter 5.2.1 --- RBF Network --- p.85 / Chapter 5.2.2 --- Experiments --- p.86 / Chapter 6 --- Conclusion and Future Work --- p.89 / Chapter 6.1 --- Conclusion --- p.89 / Chapter 6.2 --- Future Work --- p.90 / Bibliography --- p.92 / Chapter A --- A Number Detection Approach for Equal-and-Isotropic Variance Clusters --- p.100 / Chapter A.1 --- Number Detection Approach --- p.100 / Chapter A.2 --- Demonstration Experiments --- p.102 / Chapter A.3 --- Remarks --- p.105 / Chapter B --- RBF Network with RPCL Approach --- p.106 / Chapter B.l --- Introduction --- p.106 / Chapter B.2 --- Normalized RBF net and Extended Normalized RBF Net --- p.108 / Chapter B.3 --- Demonstration --- p.110 / Chapter B.4 --- Remarks --- p.113 / Chapter C --- Adaptive RPCL-CLP Model for Financial Forecasting --- p.114 / Chapter C.1 --- Introduction --- p.114 / Chapter C.2 --- Extraction of Input Patterns and Outputs --- p.115 / Chapter C.3 --- RPCL-CLP Model --- p.116 / Chapter C.3.1 --- RPCL-CLP Architecture --- p.116 / Chapter C.3.2 --- Training Stage of RPCL-CLP --- p.117 / Chapter C.3.3 --- Prediction Stage of RPCL-CLP --- p.122 / Chapter C.4 --- Adaptive RPCL-CLP Model --- p.122 / Chapter C.4.1 --- Data Pre-and-Post Processing --- p.122 / Chapter C.4.2 --- Architecture and Implementation --- p.122 / Chapter C.5 --- Computer Experiments --- p.125 / Chapter C.5.1 --- Data Sets and Experimental Purpose --- p.125 / Chapter C.5.2 --- Experimental Results --- p.126 / Chapter C.6 --- Conclusion --- p.134 / Chapter D --- Publication List --- p.135 / Chapter D.1 --- Publication List --- p.135

Submitted by Guilherme Aparecido Santos Aguilar null (guiaguilar@hotmail.com) on 2017-03-24T20:21:32Z No. of bitstreams: 1 dissertacao.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-03-27T17:03:00Z (GMT) No. of bitstreams: 1 aguilar_gas_me_prud.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) / Made available in DSpace on 2017-03-27T17:03:00Z (GMT). No. of bitstreams: 1 aguilar_gas_me_prud.pdf: 1514798 bytes, checksum: 2336853543dbc4bd478bff182d7bc837 (MD5) Previous issue date: 2017-03-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Devido aos inúmeros campos para aplicações na Análise de Sobrevivência, diferentes funções de risco são necessárias para modelar os mais diversos casos em estudo. Portanto, ao criar novas distribuições pode-se obter diferentes funções de risco com suas diferentes curvas, que podem ser utilizadas para diversos tipos de dados. Serão apresentadas três novas distribuições de probabilidade, criadas a partir de três diferentes métodos, sendo a Gama Exponenciada Estendida de Marshall Olkin, Gama Exponenciada Poisson Truncada no Zero e também a Gama Exponenciada Bivariada. Para as distribuições de probabilidade univariadas foram obtidos resultados probabilísticos, tais como o n-ésimo momento; r-ésimo momento de vida média residual; r-ésimo momento de vida média residual invertido; ordenação estocástica; entropias; desvios médios; curvas de Bonferroni e de Lorenz; assimetria, curtose e seus gráficos; estatísticas de ordem e parâmetro stress − strength. Em relação a distribuição Gama Exponenciada Bivariada foi encontrada sua função acumulada; função densidade; função marginal; função condicional e seu n-ésimo momento. Para as novas distribuições univariadas encontradas, também foram feitas simulações para diferentes valores de parâmetros com o intuito de verificar qual o melhor método de estimação, para cada parâmetro de cada distribuição. Os métodos utilizados foram: estimador de máxima verossimilhança, Mínimos Quadrados, Mínimos Quadrados Ponderados, Cramér-von-Mises, Anderson Darling, Anderson Darling -RT (cauda à direita), Anderson Darling - LT (cauda à esquerda), Anderson Darling - 2LT (cauda à esquerda de segunda ordem), Kolmogorov e também foi utilizado o método Bayesiano com priori Gama. Por último foram também realizadas aplicações em um banco de dados, uma para cada distribuição univariada, onde foi comparado o ajuste das novas distribuições propostas com outras já conhecidas na literatura. / Due to the many fields for applications in Survival Analysis, different hazard functions are needed to modelling the various case studies. Therefore, creating new distributions can obtains different hazard functions with different graphics, which can be used for various types of data. There will be presented three new probability distributions, created from three different methods, the Marshall Olkin Extendet Exponentiated Gamma, Poisson Zero Truncated Exponentiated Gamma and the Bivariate Exponentiated Gamma. For such univariate probability distributions it will be obtained some probabilistics results, like n-th time, rth moment of residual life, r-th moment of residual life inverted, stochastic ordering, entropies, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics and stress-strength parameter. Regarding the Bivariate Gamma Exponentiated was found your acumulated and density function; marginal function; conditional function and it’s n-th moment. For the new univariate distributions found, were also made simulations for different parameter values in order to find the best estimation method for each parameter. The methods used were: maximum likelihood, ordinary least-squares, weighted least-squares, Cramér-von-Mises, Anderson Darling, Anderson Darling - RT (right-tail), Anderson Darling - LT (left-tail), Anderson Darling - 2LT (left-tail second order), Kolmogorov and bayesian estimator with the prior Gamma. Some techniques to compare the estimators were used. Finally, applications were also performed, one for each univariate distribution, where the adjustment of some proposed distributions in relation to the database was tested.

Four families of contagious distributions--generalized Poisson distributions, generalized binomial distributions, generalized Pascal distributions, and generalized log-zero distributions--are investigated in this thesis. The family of generalized Poisson distributions contains five distributions: the Neyman Type A, the "Short," the Poisson binomial, the Poisson Pascal, and the negative binomial. The family of generalized binomial distributions contains eight distributions: the binomial Poisson, the binomial binomial, the binomial Pascal, the binomial log-zero, the Poisson with zeros, the binomial with zeros, the Pascal with zeros, and the log-zero with zeros. The family of generalized Pascal distributions contains four distributions: the Pascal Poisson, the Pascal binomial, the Pascal Pascal, and the Pascal log-zero. The family of generalized log-zero distributions contains four distributions: the log-zero Poisson, the log-zero binomial, the log-zero Pascal, and the log-zero log-zero. For each family of contagious distributions, the common probability generating function based on a biological model is derived by application of Feller's compound distribution theorem and Gurland's generalized distribution terminology. The common recurrence relation and the common factorial moments or cumulants are derived from the common probability generating function by using the successive differentiation method. Then for each distribution within this family, the particular probability generating function, recurrence relation, and factorial moments or cumulants are easily obtained from common ones. The equations of factorial moments or cumulants are solved. The maximum likelihood equations are derived for some distributions which have been shown to provide a good or excellent moment fitting. These equations are solved by an iteration procedure, Except for the Neyman Type A distribution and the "Short" distribution in which the maximum likelihood equations are derived from the probability generating functions and solved by the method of scoring, the maximum likelihood equations a re derived from the probability functions and solved by the Newton-Raphson method. Forty sets of biological and accident data classified into five types have been collected from various sources. A Fortran program has been written for fitting each distribution and a numerical example is given to illustrate the fitting procedure. In comparing the fits among these distributions, the chi-square goodness- of-fit values have been calculated and tabulated. The results suggest that the binomial distribution with zeros and the Pascal distribution with zeros be used if one is to describe the empirical data arising from populations having a contagious character. This is not only due to the fact that the two distributions have provided better fits to all five types of data, but also the fact that their maximum likelihood estimate procedures have no common disadvantages of other distributions. These disadvantages are that not every moment estimate can allow the iteration process to converge and that the probabilities must be recalculated after each iteration.

In the dissertation, a monotone spline-based nonparametric estimation method is proposed for analyzing longitudinal data with mixture distributions. The innovative and efficient algorithm combining the concept of projected Newton-Raphson algorithm with linear mixed model estimation method is developed to obtain the nonparametric estimation of monotone B-spline functions. This algorithm provides an efficient and flexible approach for modeling longitudinal data monotonically. An iterative 'one-step-forward' algorithm based on the K-means clustering is then proposed to classify mixture distributions of longitudinal data. This algorithm is computationally efficient, especially for data with a large number of underlying distributions. To quantify the disparity of underlying distributions of longitudinal data, we also propose an index measure on the basis of the aggregated areas under the curve (AAUC), which makes no distributional assumptions and fits the theme of nonparametric analysis. An extensive simulation study is conducted to assess the empirical performance of our method under different AAUC values, covariance structures, and sample sizes. Finally, we apply the new approach in the PREDICT-HD study, a multi-site observational study of Huntington Disease (HD), to explore and assess clinical markers in motor and cognitive domains for the purpose of distinguishing participants at risk of HD from healthy subjects.

No description available.

In this thesis, we are interested in the modelling of queueing networks with finite buffers and with general service time distributions. Queueing networks models have shown to be very useful tools to evaluate the performance of complex systems in many application fields (manufacturing, communication networks, traffic flow, etc.). In order to analyze such networks, the original distributions are most often transformed into tractable distributions, so that the Markov theory can then be applied. Our main originality lies in this step of the modelling process. We propose to discretize the original distributions by probability mass fitting (PMF). The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval. PMF has the advantage to be simple, refinable, and to conserve the shape of the distribution. Moreover, we show that it does not require more phases, and thus more computational effort, than concurrent methods. From the distributions transformed by PMF, the evolution of the system can then be modelled by a discrete Markov chain, and the performance of the system can be evaluated from the chain. This global modelling method leads to various interesting results. First, we propose two methodologies leading to bounds on the cycle time of the system. In particular, a tight lower bound on the cycle time can be computed. Second, probability mass fitting leads to accurate approximation of the performance measures (cycle time, work-in-progress, flow time, etc.). Together with the bounds, the approximations allow to get a good grasp on the exact measure with certainty. Third, the cycle time distribution can be computed in the discretized time and shows to be a good approximation of the original cycle time distribution. The distribution provides more information on the behavior of the system, compared to the isolated expectation (to which other methods are limited). Finally, in order to be able to analyze larger networks, the decomposition technique can be applied after PMF. We show that the accuracy of the performance evaluation is still good, and that the ability of PMF to accurately estimate the distributions brings an improvement in the application of the decomposition. In conclusion, we believe that probability mass fitting can be considered as a valuable alternative in order to build tractable distributions for the analytical modelling of queueing networks.

<p>Queueing models have been used extensively in the design of call centres. In particular, a queueing model will be used to describe a help desk which is a form of a call centre. The design of the queueing model involves modelling the arrival an service processes of the system.</p><p>Conventionally, the arrival process is assumed to be Poisson and service times are assumed to be exponentially distributed. But it has been proposed that practically these are seldom the case. Past research reveals that the log-normal distribution can be used to model the service times in call centres. Also, services may involve stages/tasks before completion. This motivates the use of a phase-type distribution to model the underlying stages of service.</p><p>This research work focuses on developing statistical models for the overall service times and the service times by job types in a particular help desk. The assumption of exponential service times was investigated and a log-normal distribution was fitted to service times of this help desk. Each stage of the service in this help desk was modelled as a phase in the phase-type distribution.</p><p>Results from the analysis carried out in this work confirmed the irrelevance of the assumption of exponential service times to this help desk and it was apparent that log-normal distributions provided a reasonable fit to the service times. A phase-type distribution with three phases fitted the overall service times and the service times of administrative and miscellaneous jobs very well. For the service times of e-mail and network jobs, a phase-type distribution with two phases served as a good model.</p><p>Finally, log-normal models of service times in this help desk were approximated using an order three phase-type distribution.</p>

Different universal methods (also called automatic or black-box methods) have been suggested to sample from univariate log-concave distributions. The description of a suitable universal generator for multivariate distributions in arbitrary dimensions has not been published up to now. The new algorithm is based on the method of transformed density rejection. To construct a hat function for the rejection algorithm the multivariate density is tranformed by a proper transformation T into a concave function (in the case of log-concave density T(x) = log(x).) Then it is possible to construct a dominating function by taking the minimum of several tangent hyperplanes which are transformed back by $T^(-1)$ into the original scale. The domains of different pieces of the hat function are polyhedra in the multivariate case. Although this method can be shown to work, it is too slow and complicated in higher dimensions. In this paper we split the $R^n$ into simple cones. The hat function is constructed piecewise on each of the cones by tangent hyperplanes. The resulting function is not continuous any more and the rejection constant is bounded from below but the setup and the generation remains quite fast in higher dimensions, e.g. n=8. The paper describes the details how this main idea can be used to construct algorithm TDRMV that generates random tuples from multivariate log-concave distribution with a computable density. Although the developed algorithm is not a real black box method it is adjustable for a large class of log-concave densities. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

<p>Queueing models have been used extensively in the design of call centres. In particular, a queueing model will be used to describe a help desk which is a form of a call centre. The design of the queueing model involves modelling the arrival an service processes of the system.</p><p>Conventionally, the arrival process is assumed to be Poisson and service times are assumed to be exponentially distributed. But it has been proposed that practically these are seldom the case. Past research reveals that the log-normal distribution can be used to model the service times in call centres. Also, services may involve stages/tasks before completion. This motivates the use of a phase-type distribution to model the underlying stages of service.</p><p>This research work focuses on developing statistical models for the overall service times and the service times by job types in a particular help desk. The assumption of exponential service times was investigated and a log-normal distribution was fitted to service times of this help desk. Each stage of the service in this help desk was modelled as a phase in the phase-type distribution.</p><p>Results from the analysis carried out in this work confirmed the irrelevance of the assumption of exponential service times to this help desk and it was apparent that log-normal distributions provided a reasonable fit to the service times. A phase-type distribution with three phases fitted the overall service times and the service times of administrative and miscellaneous jobs very well. For the service times of e-mail and network jobs, a phase-type distribution with two phases served as a good model.</p><p>Finally, log-normal models of service times in this help desk were approximated using an order three phase-type distribution.</p>

The variation of velocity and temperature distribution in arbitrary profile along the centerline in turbulent which encounters non-linearity regular progressive gravity wave and steady uniform flow right in front are investigated analytically and verified by existing experiments. Firstly, the action of periodic waves and current are incorporated into the equation of motion as an external force and applied radiation stress for evaluating the velocity distribution over arbitrary lateral cross section. Based on the momentum exchange after the interaction between turbulent plane jet and oppositive non-linearity wave and uniform flow, the physical characteristics of jet-wave and current are able to be determined theoretically. Secondly, there are critical sections in both velocity and temperature transport processes when the turbulent plane jet influenced by wave and current motion. Fluctuating function will be close to infinity, is the order of wave sharpness; Average velocity for every wave period along the centerline approach to zero, That¡¦s thanks to the momentum of plane jet is extruded by the momentum of wave and current, Beyond the critical section, characteristics of the jet is no longer existing, such phenomena mean that only the wave and current dominating. Velocity and temperature distribution in the zone of flow developed are Gaussian curve, as has been measured in experiment. The momentum extrusion of counter flow in jet is significant in the deep water and small wave; The velocity distribution coefficient is changing with the increasing of counter flow velocity, owing to the entrainment effect, and the potential core will reducing with the increasing of counter flow velocity.